1. Technical Field
The present invention relates to a laminated half-wave plate in which two wave plates formed of an inorganic crystalline material such as quartz crystal having birefringence properties are arranged to overlap with each other, and an optical pickup device, a polarization converter, and a projection display apparatus which employ the laminated half-wave plate.
2. Related Art
A half-wave plate emitting as an output beam a linearly-polarized beam obtained by rotating a polarization plane of a linearly-polarized beam of an incident beam by a predetermined angle, for example, 90°, has been employed in optical devices such as an optical pickup device used for recording on and reproduction from an optical disk device, a polarization converter, and a projection display apparatus such as a liquid crystal projector. As for the half-wave plate, various laminated structures have been suggested in which two wave plates are bonded so that their optical axes intersect.
In general, a half-wave plate has wavelength dependence where phase difference varies with a variation in wavelength, and the phase difference increases or decreases in wavelength bands in the vicinity of a target wavelength. In the half-wave plate used in a polarization converter of a liquid crystal projector, it is required that the phase difference of 180° is kept in a broad wavelength range of 400 to 700 nm. Therefore, a laminated wave plate is known (for example, JP-A-2004-170853) where the whole of which serves as a half-wave plate in the above-mentioned broad wavelength range and is formed by bonding a first wave plate with an optical axis bearing angle θ1 and a second wave plate with an optical axis bearing angle θ2 so that the optical axes thereof intersect each other and satisfy the relations of θ2=θ1+45° and 0<θ1<45°.
In a liquid crystal projector or an optical pickup device, since a beam diverges and is incident on the half-wave plate, there is a problem with the incident angle dependence that the phase difference varies in regions other than the vicinity of the center of the wave plate. Accordingly, a polarization conversion efficiency of a half-wave plate, that is, a ratio at which the incident linearly-polarized beam of P polarization is converted into a linearly-polarized beam of S polarization and the resultant beam is output, is lowered, thereby causing a loss of light intensity. Therefore, a high-order-mode laminated wave plate is known where the whole of which serves as a half-wave plate in which a first wave plate with a phase difference of Γ1=180°+360°×n (where n is a positive integer) and a second wave plate with a phase difference of Γ2=180°+360°×n are bonded so that the optical axes thereof intersect each other and θ2=θ1+θ/2 is satisfied, where in-plane bearing angles of the first and second wave plates are represented by θ1 and θ2 and an angle formed by the polarization direction of the linearly-polarized beam incident on the laminated wave plate and the polarization direction of the linearly-polarized beam output therefrom is represented by θ (For example, JP-A-2007-304572).
In JP-A-2007-304572, by appropriately setting n of the first and second wave plates of the laminated wave plate, the thickness can be set to a size which can be easily machined. By setting n=5, θ1=22.5°, and θ2=67.5° in the laminated wave plate, the wavelength conversion efficiency can be set to almost 1 in the wavelength bands 405 nm, 660 nm, and 785 nm required for the three-band optical pickup wave plate for three primary colors of red, blue, and green light, thereby suppressing the loss in light intensity.
Similarly, to improve the polarization conversion efficiency, a laminated wave plate is suggested which serves as a half-wave plate in which a first wave plate with a phase difference Γa=180° and a second wave plate with a phase difference Γb=180° are bonded, the optical axis bearing angles θa and θb of the first and second wave plates satisfy θb=θa+α, 0<θa<45°, and 40°<α<50°, and a difference ΔΓa of the phase difference Γa from a designed target value and a difference ΔΓb of the phase difference Γb from a designed target value satisfy a predetermined relational expression (see JP-A-2008-268901). In this laminated wave plate, by canceling the difference ΔΓa of the phase difference Γa from the designed target value with the difference ΔΓb of the phase difference Γb from the designed target value on the basis of the predetermined relational expression, it is possible to obtain a high polarization conversion efficiency.
FIGS. 16A and 16B are diagrams illustrating a typical example of the above-mentioned laminated half-wave plate according to the related art. The laminated half-wave plate 1 includes first and second wave plates 2 and 3 which are formed of an optical uniaxial crystalline material such as a quartz crystal substrate and which are arranged sequentially from the light incidence side Li to the light output side Lo. The first and second wave plates are bonded so that crystal optical axes 4 and 5 thereof intersect each other at a predetermined angle. At this time, the phase difference of the first wave plate 2 is Γ1=180°+n1×360° (where n1 is a non-negative integer) and the phase difference of the second wave plate 3 is Γ2=180°+n2×360° (where n2 is a non-negative integer). The optical axis bearing angle θ1 of the first wave plate 2 is an angle formed by the crystal optical axis 4 and the polarization plane of the linearly-polarized beam 6 incident on the laminated half-wave plate 1 and the optical axis bearing angle θ2 of the second wave plate 3 is an angle formed by the crystal optical axis 5 and the polarization plane of the linearly-polarized beam.
In the laminated half-wave plate 1 shown in FIGS. 16A and 16B, the angle formed by the polarization direction of the incident linearly-polarized beam 6 and the polarization direction of the output linearly-polarized beam 7 is set to 90°. The polarization state of the laminated half-wave plate 1 is described now using a Poincare sphere shown in FIGS. 17A to 17C. FIG. 17A is a diagram illustrating a trajectory transition in the Poincare sphere of the linearly-polarized beam incident on the laminated half-wave plate 1. A position in the equatorial line at which the linearly-polarized beam 4 is incident is set to an intersection point P0 with an axis S1. FIG. 17B is a view illustrating the locus of the polarization state of a beam incident on the laminated half-wave plate 1 as viewed from an axis S2 in the Poincare sphere shown in FIG. 17A, that is, a projected diagram onto the plane S1S3. FIG. 17C is a view illustrating the locus of the polarization state of a beam incident on the laminated half-wave plate 1 as viewed from an axis S3 in the Poincare sphere shown in FIG. 17A, that is, a projected diagram onto the plane S1S2.
The reference point of the incident beam is set to a point P0=(1, 0, 0) in the axis S1, the rotation axis R1 of the first wave plate 2 is set to a position which is rotated from the axis S1 by 2θ1, and the rotation axis R2 of the second wave plate 3 is set to a position which is rotated from the axis S1 by 2θ2. When the reference point P0 is rotated about the rotation axis R1 to the right side by the phase difference Γ1, the point P1=(0, 1, 0) in the equatorial line of the Poincare sphere is the position of the output beam of the first wave plate 2. When the point P1 is rotated about the rotation axis R2 to the right side by the phase difference Γ2, the point P2=(−1, 0, 0) in the equatorial line of the Poincare sphere is the position of the output beam of the second wave plate 3, that is, the position of the output beam of the laminated half-wave plate 1. As long as the wavelength of the incident beam Lo does not depart from the target value, the position of the output beam is located in the equatorial line of the Poincare sphere.
However, an optical pickup device mounted on a blu-ray optical disk recording and reproducing apparatus employs a short-wavelength (405 nm) violet-blue laser. When it expands due to the high temperature when being used, a problem is caused in that the wavelength of an oscillated laser drifts. Accordingly, in the optical pickup device, the half-wave plate causes a problem that the conversion efficiency of the linearly-polarized beam is deteriorated due to the wavelength drift of the incident laser beam. Particularly, when the half-wave plate is in a high-order mode described in JP-A-2007-304572, the thickness is great and thus the variation increases with an increase in phase difference, thereby further deteriorating the conversion efficiency.
JP-A-2004-170853 discloses a method for preventing or reducing the influence of the variation in wavelength. In this method, when the differences of the phase differences of the first and second wave plates due to the variation in wavelength are ΔΓ1 and ΔΓ2, the differences of the phase differences can be canceled by setting ΔΓ1=ΔΓ2. Accordingly, the position P2 of the output beam in the Poincare sphere is always located in the equatorial line.
This will be described using the Poincare sphere shown in FIGS. 17A to 17C. The position of the output beam of the first wave plate 2 is the point P1′ which is rotated about the rotation axis R1 from the point P1 to the right side by the difference ΔΓ1. The position of the output beam of the second wave plate 3 is the point P2′ in the equatorial line of the Poincare sphere which is rotated about the rotation axis R2 from the point P1′ to the right side by the difference Γ2+ΔΓ2. The point P2′ is the position of the output beam from the laminated half-wave plate 1. As can be seen from the drawings, since the point P2′ is deviated from the point P2 in the equatorial line, the rotation of the polarization plane of the output beam is deviated from 90°.
In JP-A-2004-170853, the rotational deviation of the polarization plane of the output beam can decrease as ΔΓ1 and ΔΓ2 decrease. Accordingly, it is preferable that the first and second wave plates 2 and 3 are formed of a single-mode wave plate and the wavelength dependency is reduced as much as possible. The single-mode wave plate with a phase difference of 180° is excellent in terms of incident angle dependency, which is desirable. However, when the wave plate is formed particularly of a quartz crystal plate with a cutting angle of 90° Z, that is, with an angle of 90° formed by a normal direction of main surface of the quartz crystal substrate and the quartz crystal optical axis (Z axis), the thickness decreases up to 20 μm and thus it is difficult to manufacture the wave plate.
JP-A-2008-268901 discloses a problem that the position of the output beam of the first wave plate in the Poincare sphere is deviated when the thickness processing accuracy of the first wave plate deviates from the designed value. To solve this problem, JP-A-2008-268901 discloses a method of processing the thickness of the second wave plate so as to cancel the deviation of the position of the output beam of the first wave plate. However, in the laminated wave plate disclosed in JP-A-2008-268901, since the first and second wave plates are also the single-mode wave plates formed of a quartz crystal plate with a cutting angle of 90° Z, it is difficult to manufacture the wave plate.
On the other hand, in the laminated half-wave plate disclosed in JP-A-2007-304572, since the first and second wave plates are in a high-order mode, there are no problems in terms of manufacturing difficulties. However, when the order n of the high-order mode of the first and second wave plates is too great, the wavelength band width in which the conversion efficiency is close to 1 is reduced and thus there is a problem in terms of difficulties with its use as the laminated half-wave plate.
Here, the conversion efficiency is an estimated value used to accurately determine the polarization state of the output beam of the laminated half-wave plate including two wave plates bonded to each other, as described in JP-A-2007-304572, and is obtained by calculating the light intensity of the output beam with respect to the incident beam by a predetermined calculation technique. This method is simply described below.
In the laminated half-wave plate 1, when the Muller matrix of the first wave plate 2 is represented by R1, the Muller matrix of the second wave plate 3 is represented by R2, the polarization state of the incident beam is represented by vector I, and the polarization state of the output beam is represented by vector E, the polarization state of the beam having passed through the laminated half-wave plate 1 can be expressed by the following expression.E=R2·R1·I  Expression 1Here, R1 and R2 are expressed by the following expressions.
                              R          1                =                  [                                                    1                                            0                                            0                                            0                                                                    0                                                              1                  -                                                            (                                              1                        -                                                  cos                          ⁢                                                                                                          ⁢                                                      Γ                            1                                                                                              )                                        ⁢                                          sin                      2                                        ⁢                    2                    ⁢                                          θ                      1                                                                                                                                        (                                          1                      -                                              cos                        ⁢                                                                                                  ⁢                                                  Γ                          1                                                                                      )                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                                      θ                    1                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                                      θ                    1                                                                                                                    -                    sin                                    ⁢                                                                          ⁢                                      Γ                    1                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    1                                                                                                      0                                                                                  (                                          1                      -                                              cos                        ⁢                                                                                                  ⁢                                                  Γ                          1                                                                                      )                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    1                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    1                                                                                                                    1                    -                                                                  (                                                  1                          -                                                      cos                            ⁢                                                                                                                  ⁢                                                          Γ                              1                                                                                                      )                                            ⁢                                              sin                        2                                            ⁢                      2                      ⁢                                              θ                        1                                                                              )                                                                              sin                  ⁢                                                                          ⁢                                      Γ                    1                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    1                                                                                                      0                                                              sin                  ⁢                                                                          ⁢                                      Γ                    1                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    1                                                                                                                                          -                      sin                                        ⁢                                                                                  ⁢                                          Γ                      1                                        ⁢                    cos                    ⁢                                                                                  ⁢                    2                    ⁢                                          θ                      1                                                        ⁢                                                                                                                                      cos                  ⁢                                                                          ⁢                                      Γ                    1                                                                                ]                                    Expression        ⁢                                  ⁢        2                                          R          2                =                  [                                                    1                                            0                                            0                                            0                                                                    0                                                              1                  -                                                            (                                              1                        -                                                  cos                          ⁢                                                                                                          ⁢                                                      Γ                            2                                                                                              )                                        ⁢                                          sin                      2                                        ⁢                    2                    ⁢                                          θ                      2                                                                                                                                        (                                          1                      -                                              cos                        ⁢                                                                                                  ⁢                                                  Γ                          2                                                                                      )                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                                      θ                    2                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                                      θ                    2                                                                                                                    -                    sin                                    ⁢                                                                          ⁢                                      Γ                    2                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    2                                                                                                      0                                                                                  (                                          1                      -                                              cos                        ⁢                                                                                                  ⁢                                                  Γ                          2                                                                                      )                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    2                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    2                                                                                                                    1                    -                                                                  (                                                  1                          -                                                      cos                            ⁢                                                                                                                  ⁢                                                          Γ                              2                                                                                                      )                                            ⁢                                              sin                        2                                            ⁢                      2                      ⁢                                              θ                        2                                                                              )                                                                              sin                  ⁢                                                                          ⁢                                      Γ                    2                                    ⁢                  cos                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    2                                                                                                      0                                                              sin                  ⁢                                                                          ⁢                                      Γ                    2                                    ⁢                  sin                  ⁢                                                                          ⁢                  2                  ⁢                                      θ                    2                                                                                                                                          -                      sin                                        ⁢                                                                                  ⁢                                          Γ                      2                                        ⁢                    cos                    ⁢                                                                                  ⁢                    2                    ⁢                                          θ                      2                                                        ⁢                                                                                                                                      cos                  ⁢                                                                          ⁢                                      Γ                    2                                                                                ]                                    Expression        ⁢                                  ⁢        3            
When the order n of the high-order mode of the first and second wave plates 2 and 3, the phase differences Γ1 and Γ2, and the optical axis bearing angles θ1 and θ2 are set, the Muller matrixes R1 and R2 are calculated by using Expressions 2 and 3, and the polarization state I of the incident beam is set, the polarization state E of the output beam is calculated by using Expression 1. The polarization state E of the output beam is called a Stokes vector and is expressed by the following expression.
                    E        =                  [                                                                      S                  01                                                                                                      S                  11                                                                                                      S                  21                                                                                                      S                  31                                                              ]                                    Expression        ⁢                                  ⁢        4            
Here, the E matrix elements S01, S11, S21, and S31 are called Stokes parameters and indicate the polarization state. When the transmission axis of a matrix P of a polarizer is set to a predetermined angle and the product of the matrix E indicating the polarization state E of the output beam and the matrix P of the polarizer is T, T is expressed by the following expression.T=P·E  Expression 5
The matrix T indicates the conversion efficiency and can be expressed by the following expression using the Stokes parameters of the elements.
                    T        =                  [                                                                      S                  02                                                                                                      S                  12                                                                                                      S                  22                                                                                                      S                  32                                                              ]                                    Expression        ⁢                                  ⁢        6            
Here, when the Stokes parameter S02 of the vector T represents the light intensity and the incident light intensity is set to 1, the Stokes parameter S02 is the conversion efficiency. Accordingly, the conversion efficiency T of the laminated half-wave plate 1 can be simulated while variously changing the order n of the high-order mode of the first and second wave plates 2 and 3, the phase differences Γ1 and Γ2 at a predetermined wavelength (for example, at a wavelength of 405 nm), and the optical axis bearing angles θ1 and θ2.
FIG. 18 shows the simulation result of the variation in conversion efficiency T with respect to the wavelength of the incident beam when the target wavelength λ0, which is used in the laminated half-wave plate 1 according to the related art shown in FIGS. 16A and 16B, is 405 nm. In the drawing, it can be seen that the conversion efficiency in the related art is almost 1 in the vicinity of λ0=405 nm, but deteriorates as the wavelength gets farther from the target value. When the laminated half-wave plate is used in the optical pickup device, the conversion efficiency of the linearly-polarized beam may deteriorate due to the wavelength drift of the incident laser beam.